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Langmuir 1997, 13, 5294-5305
Nonlinear Hairy Layer Theory of Electrophoretic Fingerprinting Applied to Consecutive Layer by Layer Polyelectrolyte Adsorption onto Charged Polystyrene Latex Particles E. Donath,†,‡ D. Walther,§ V. N. Shilov,| E. Knippel,*,† A. Budde,† K. Lowack,⊥ C. A. Helm,⊥,X and H. Mo¨hwald‡ Medical School, University of Rostock, Ernst-Heydemann-Strasse 6, P.O. Box 100888, 18055 Rostock, Germany, Max-Planck-Institut fu¨ r Kolloid- & Grenzfla¨ chenforschung, Haus 9.9, Rudower Chaussee 5, 12489 Berlin, Germany, EMBL, Meyerhofstrasse 1, 69012 Heidelberg, Germany, Institute of Biocolloid Chemistry, Ukrainian Academy of Science, Kiev, Ukraine, Institut fu¨ r Physikalische Chemie, Johannes-Gutenberg-Universita¨ t, Jacob-Welder-Weg 11, 55099 Mainz, Germany, and Fachrichtung Strukturforschung, Universita¨ t des Saarlandes, Postfach 151150, 66041 Saarbru¨ cken, Germany Received January 29, 1997. In Final Form: July 11, 1997X The consecutive layer-by-layer adsorption of poly(allylamine hydrochloride) (PAH) and poly(styrenesulfonate) (PSS) on colloidal charged latex particles is investigated by measuring the electrophoretic mobility as a function of pH and ionic strength over a broad range (electrophoretic fingerprinting). Meaningful interpretation of the data required the development of a nonlinear approach to hairy particle electrophoresis including dissociation, adsorption, and association. Steric and electrostatic exclusion of mobile ions from the hairy layer has been considered. Also, the surface conductivity correction is extended to the case of charged hairy layer particles. We deposited up to three polyelectrolyte layers. The following were found: (i) Each layer deposition is accompanied by charge overcompensation and (ii) Not only the top layer but also the underneath layers and the naked latex particle surface contribute to the particle mobility. This can be interpreted as an incomplete coverage or a polyelectrolyte interpenetration. (iii) The thickness of the top adsorbed hairy layer is of the order of 1 nm. (iv) About one-third of the charged groups of the top layer form ion pairs with the underneath charges. (v) Counterion adsorption to the charged groups of the top layer can be observed.
Introduction The consecutive alternating deposition of oppositely charged polymers onto a variety of surfaces has recently met increasing interest. It has been demonstrated that a number of different polymers and biopolymers with various functional sites are able to form polyelectrolyte multilayers on charged substrates.1-3 This has been shown by means of optical, X-ray, and neutron scattering experiments4-7 as well as electrophoretic experiments8 at constant ionic strength revealing stable multilayers of highly charged polyions. The thickness of the individual layers depends on the deposition conditions and is of the order of one to a few nanometers.6 Yet less is known about the electrostatic properties of these layers, although this knowledge is crucial for many applications where interac* To whom correspondence should be addressed. † University of Rostock. ‡ Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. § EMBL. | Ukrainian Academy of Science. ⊥ Johannes-Gutenberg-Universita ¨ t. X Universita ¨ t des Saarlandes. X Abstract published in Advance ACS Abstracts, September 15, 1997. (1) Decher, G.; Lehr, B.; Lowack, K.; Lvov, Y.; Schmitt, J. Biosens. Bioelectron. 1994, 9, 677. (2) Kleinfeld, E. R.; Ferguson, G. S. Science 1994, 265, 370. (3) Lvov, Y.; Ariga, K.; Kunitake, T. J. Am. Chem. Soc. 1995, 117, 6117. (4) Schmitt, J.; Gru¨newald, T.; Kjaer, K.; Pershan, P.; Decher, G.; Lo¨sche, M. Macromolecules 1993, 26, 7058. (5) Decher, G.; Hong, J. D.; Schmitt, J. Thin Solid Films 1992, 210/ 211, 831. (6) Lvov, Y.; Decher, G.; Mo¨hwald, H. Langmuir 1993, 9, 481. (7) Lvov, Y.; Decher, G.; Haas, H.; Mo¨hwald, H.; Kalachev, A. Physica B 1994, 244, 89. (8) Hoogeveen, N. G.; Cohen Stuart, M. A.; Fleer, G. J. Langmuir 1996, 12, 3675.
S0743-7463(97)00090-5 CCC: $14.00
tion processes between surfaces or charged molecules take place. The question of surface charge is also of high technical relevance considering the interaction of latices, e.g., in films. Yet, little is known in this field. For instance, available equilibrium thermodynamic models do not predict a strong overcompensation of the electric potential.9,10 But it has been shown recently that polyelectrolyte adsorption is accompanied by an overcompensation of the detectable electric potential.8,11-13 It is not clear to what extent the top layer alone determines the surface potential. The charge overcompensation has led to the rather simple conclusion that the underlying layers have only a limited influence on the surface potential observed with electrophoresis. An understanding of how the charge of the support influences the electric properties of the complete system is important for the optimal design of layer structures because in most cases it is not desired to have electric contributions from the support. From scattering experiments it is well known that the thickness of the layers is a function of deposition conditions such as salt6 and polyelectrolyte14 concentration. It is not known whether this is reflected in the resulting surface potentials, too. By means of fluorescence spectroscopy, local internal electric potentials were found to depend strongly on the (9) van de Steeg, H. G. M.; Cohen Stuart, M. A.; Keizer, A. D.; Bijsterbosch, B. H. Langmuir 1992, 8, 2538. (10) Cohen Stuart, M. A.; Fleer, G. J.; Lyklema J., Norde, W.; Scheutjens, J. M. H. M. Adv. Colloid Interface Sci. 1991, 34, 477. (11) Berndt, P.; Kurihara, K.; Kunitake, T. Langmuir 1992, 8, 2486. (12) Claesson, P. M.; Dahlgren, M. A. G.; Eriksson, L. Colloids Surf., A 1994, 93, 293. (13) Hoogeveen, N. In Adsorption of Polyelectrolytes and charged block copolymers on oxides. Consequences for colloidal stability. Thesis, Landbouwuniversiteit Wageningen, 1996. (14) Polyelectrolyte concentration influences layer thickness.
© 1997 American Chemical Society
Electrophoretic Fingerprinting
charge of the outer layer.15 From measurement of the interaction force between polyelectrolyte-covered mica surfaces, information about the distance dependence of the electric potential has been obtained.16-18 Although these techniques have provided valuable information, a number of questions remain open since both methods measure the surface potential of the polymer multilayer structures at different planes of origin. For example, to interpret experiments with potential-sensitive fluorescence labels, the polarity of the label environment has to be known. Interaction forces between surfaces do not provide information on the sign of the electrostatic potential. Since no analytical electrostatic theory for thick charged layers consisting of hairy polyelectrolytes is available, until now simplified surface potential theories have been applied for the interpretation of the various experimental data. Electrophoretic investigations can provide information on the surface potential, the surface charge of particles. Equally important for the interpretation of electrophoretic mobility data are the hydrodynamic properties of the outermost region of the interface. Thus electrophoretic measurements can provide valuable insights into the interfacial hydrodynamics within a nanometer range.19-21 The surface conductivity is another parameter modifying the electrophoretic mobility which is especially important under conditions of low ionic strengths and high surface charge density. Recent progress in the linear theory of electrophoresis of charged layer structures provided information regarding the charge distribution within a weakly charged grafted polyelectrolyte layer adjacent to biological surfaces.22 Yet, it is still difficult to predict from electrophoretic experiments alone the electrostatic interfacial properties because in most cases the number of unknown parameters such as the hairy layer thickness, the density profile of the fixed charges, the hydrodynamic resistance of the layers, as well as the surface conductivity is too large to allow a unique interpretation of electrophoretic data. One way to minimize the number of these unknown parameters is to use molecular considerations to obtain reasonable estimates for layer thickness and charge density distribution as a function of the distance from the surface. It is not sufficient to measure the mobility as a function of pH alone because deeper regions of the charged layer structures contribute to the electrophoretic mobility only at sufficiently low ionic strength where the Debye length is comparable with or larger than the thickness of the polyelectrolyte layer. The systematic measurement of the mobility as a function of both the pH and ionic strength (conductivity), called electrophoretic fingerprinting,23 has been used below to explore the electrostatic properties of poly(styrenesulfonate) (PSS) and poly(allylamine hydrochloride) (PAH) deposited on poly(styrene sulfate) latex particles. In contrast to biological surfaces these synthetic polyelectrolytes are highly charged. For this reason the equations obtained with the linearization of the Poisson(15) von Klitzing, R.; Mo¨hwald, H. Langmuir 1995, 11, 3554. (16) Dahlgren, M. A. G.; Waltermo, A.; Blomberg, E.; Claesson, P. M.; Sjo¨stro¨m, L.; Akesson, T.; Jo¨nsson, B. J. Phys. Chem. 1993, 97, 11769. (17) Claesson, P. M.; Ninham, B. W. Langmuir 1992, 8, 1406. (18) Lowack, K.; Helm, C. A. Submitted for publication in Macromolecules. (19) Donath, E.; Voigt, A. J. Colloid Interface Sci. 1986, 109, 122. (20) Donath, E.; Krabi, A.; Allan, G.; Vincent, B. Langmuir 1996, 12, 3425. (21) Oshima, H. Adv. Colloid Interface Sci. 1995, 62, 189. (22) Donath, E.; Budde, A.; Knippel, E.; Ba¨umler, H. Langmuir 1996, 12, 4832. (23) Marlow, B. J.; Rowell, R. L. Langmuir 1990, 6, 1088.
Langmuir, Vol. 13, No. 20, 1997 5295
Boltzmann equation do not describe the electrophoretic fingerprinting data sufficiently. In the case of highly charged surfaces it is essential to consider the influence of the surface conductance on the electrophoretic mobility.24 So far a theory providing the surface conductivity correction of the mobility for surfaces with charged hairy layers does not exist. Since the adsorbed polyelectrolyte layers may not lay flat on the surface, the volume concentration of the polymer segments in the hairy layer is not negligible, for an appropriate electrostatic description one has to account for steric small ion exclusion and layer polarity changes as well. To overcome these restrictions of the previous linear theory, a computer-time-saving numerical procedure providing the solution of the nonlinear electrostatic problem has been developed. The hydrodynamic friction coefficient of the layer is expressed in terms of molecular properties of the layer such as volume fraction and diameter of the layer forming polymers. The extended concept, however, is still restricted to the case of large particles as compared to the Debye length and the charged layer thickness. In a first series of experiments we measure electrophoretic fingerprints of positively charged PAH and negatively charged PSS deposited onto negatively charged latex particles starting with positively charged PAH. Up to three layers are successively deposited and the fingerprints are used to explore the electrostatic properties of these intermediate layer structures. Attempts to use an uncharged latex particle as the initial surface for the PSS or PAH deposition failed. No stable layers were formed; desorption depending on storage conditions took place. The use of a negatively charged polystyrene latex guaranteed stable adsorption layers. Theory and Numerics It is now well accepted that the electrophoretic mobility µ of a particle with a hairy surface layer cannot be described by means of the Helmholtz/Smoluchowski equation valid only for smooth surfaces with fixed charges arranged in a plane
µ)
ν 0ζ ) E η
(1)
Here ν is the electrophoretic velocity, E is the electric field strength, η is the viscosity, and and 0 are the relative and absolute dielectric permittivities, respectively. The Smoluchowsky equation essentially provides the definition for the zeta potential, ζ. In the case of a smooth surface the zeta potential is the electric potential difference between the plane of shear and infinity. In the absence of a well-defined plane of shear, which is the case for particles covered with hairy layers, the definition of the zeta potential is more complicated. A new description of the electrophoretic properties of surfaces with hairy layers is required. To solve the problem of the electrophoretic mobility of a particle covered with a charged hairy layer, we make use of Onsager’s law in order to replace the problem of calculating the electrophoretic mobility by the calculation of the streaming current near a hypothetical hairy surface in a rectangular chamber.25 This approach has the advantage of conveniently separating the hydrodynamic and the electrostatic part of the problem. Indeed, the (24) Donath, E.; Voigt, A. Biophys. J. 1986, 49, 493. (25) Voigt, A.; Donath, E.; Kretzschmar, G. Colloids Surf. 1990, 47, 23.
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magnitude of the electrophoretic velocity of a particle is equal to the electroosmotic velocity of the flow at infinite distance from the particle surface. On the other hand, the electroosmotic velocity coefficient represents one of the cross coefficients on Onsager’s flow matrix, L12.
is its charge number, and Xi is the steric exclusion factor with Xi ) 1 for x > δ. Equation 4 becomes
d2ψ ) dx2
J ) L11∆p + L12∆ψ
1 -
I ) L21∆p + L22∆ψ
I)
∫0∞ Fmob(x) ν(x) dx
Fm(x)
m
0 i
2
}
(5)
(6)
The numerical procedure presented below includes furthermore adsorption of ions to neutral sites as well as ion association to charged sites. Equation 5 represents a nonlinear differential equation of second order with the boundary conditions
dψ σ , )dx 0 a
x)0
dψa dψi ) i , dx dx
ψ)
dψ ) 0, dx
(7)
x)δ xf∞
(8)
(9)
σ denotes the surface charge density in the plane x ) 0. The indices a and i denote electric potential and dielectric permittivity outside and inside the layer, respectively. Assuming symmetrical electrolytes, eq 3 outside the charged layer can be easily integrated providing the wellknown expression for the first integral of the nonlinear Poisson-Boltzmann equation:
2kTNA 0
∑i ci (e-z e ψ/kT - 1)1/2 ) 0 i 0
(10)
with ψψ′ < 0 Inside the layer the nonlinear differential equation (5) is solved numerically as follows. Suppose there is a function ψ*(x) satisfying the boundary conditions (7) and (8) which is sufficiently close to the solution ψ(x). ψ(x) and its derivatives can now be expanded in a Taylor series. The coefficients of expansion are calculated at ψ*(x). This approach transforms eq 5 into a linear differential equation with respect to ψ(x)
ψ′′(x) - g(x)ψ(x) ) f(x),
x δ. The pK of the mth group is pKm. zm is the valence of the ion dissociated from or adsorbed to the mth group. The charge density corresponding to the distribution of the mobile ions is given by the Boltzmann distribution. ci is the concentration of the ith ionic species of the electrolyte. zi
1 + 10zm(pKm-pH-(e0ψ(x)/ln 10kT))
Here e0, k, T, and NA are elementary charge, Boltzmann constant, absolute temperature, and Avogadro’s constant, respectively. The steric exclusion factor X describes the ion partition between the polyelectrolyte layer and the bulk. It depends on the polyelectrolyte density, the mesh size of the layer, and the solvated ion radius, ri. For the case of cylindrical polymers of radius rp and sufficiently small polymer volume fractions, v, the steric exclusion factor is approximatively given by27
ψ′ + sign(ψ)
2
]
1
NAe0
(3)
Fmob(x) is the equilibrium charge density given by the Boltzmann distribution of mobile ions according to the electric potential profile ψ(x). The electrophoretic mobility is obtained by the streaming current divided by the pressure gradient and the chamber width. Below we assume throughout that the radius of the particle is large as compared to the Debye length, 1/κ, and the thickness of the charged layer consisting of polyelectrolyte chains is denoted by δ. We assume uniform charge distribution in the lateral direction but allow for arbitrary distribution of the polyelectrolyte-borne charges perpendicular to the surface. Electrostatics of the Hairy Layer. In the approximation of thin double layers we have the onedimensional Poisson equation for the electric potential ψ(x).
F(x) dψ )2 0 dx
0
(2)
L11 has the meaning of the hydrodynamic conductance of the hypothetic rectangular chamber. L21 is the streaming current coefficient and L22 represents the electric conductance of the system. ∆p is the hydrostatic pressure difference. J and I are charge and volume flow, respectively. Onsager’s law L12 ) L21 proves that the streaming current is apart from a normalizing coefficient identical to the electrophoretic mobility. The electrostatic part consists of calculating the electric potential ψ(x) as a function of distance from the particle surface. x denotes the coordinate perpendicular to the interface with the origin placed at the particle surface. Hydrodynamics provide the convective flow velocity ν(x) in the hypothetical rectangular chamber driven by the pressure difference ∆p applied along the chamber.26 The streaming current is given by the flow of ions transported by a convective flow parallel to the surface under study. Thus the streaming current per unit width of the chamber is equal to
{∑ [
(27) Schnitzer, J. E. Yale J. Biol. Med. 1988, 61, 427.
(11)
Electrophoretic Fingerprinting
g(x) ) e0 -
{∑ [
0kT
Fm(x)
zm10zm(pKm-pH-(e0ψ*(x)/ln 10 kT))
(1 + 10zm(pKm-pH-(e0ψ*(x)/ln 10 kT)))2
m
NAe0 and
f(x) ) -
1
{
0
Langmuir, Vol. 13, No. 20, 1997 5297
Fm(x) ∑ m NAe0
∑i cizi2Xie-e z ψ*(x)/kT 0 i
[
]
(12)
1
1 + 10zm(pKm-pH-(e0ψ*(x)/ln 10 kT))
}
∑i ciziXie-z e ψ*(x)/kT i 0
-
]
+
- g(x)ψ (13)
with the boundary conditions
ψ′ t 0,
x)0
(14)
and
into eq 3, we find the contribution of the inner layer flow to the electrophoretic mobility of the particle. Then, the analytically derived contribution of the double layer outside the polyelectrolyte layer is added. Surface Conductivity. Especially, if thick and highly charged layers are considered, it becomes necessary to correct the mobility for surface conductivity. The surface conductivity consists of the migrative and convective part. The migration contribution, Km, is given by the excess spatial density of the mobile ions in the double layer compared to the bulk
Km ) NA
∑i zie0ci ∫0
∞
(uiXie-zie0ψ(ξ)/kT - uibulk) dξ (21)
Here ui denotes the mobility of the ith ionic species. As a first approximation we shall equate the ionic mobility within the layer to its bulk value, ubulk. The convective part of the surface conductivity Kc is given by
1 E
Kc )
∫0∞ ν(x)Fmob(x) dx
(22)
2
ψ′(x)ψ*′(x) + ψ(x)h(x) ) (ψ*′(x)) + ψ*h(x), x)δ
(15)
Here ν(x) is the electroosmotic flow velocity and is given by the solution of
ν(x)′′ - a2ν(x) ) EFmob(x)
with
h(x) )
a NAe0 2
i
0
∑i ciziXie-z e ψ*/kT i 0
(16)
∑i ciziXie-z e ψ(x)/kT i 0
(17)
Hydrodynamics. The convective velocity is given by the Navier-Stokes equation
d2ν(x) dx2
- a2ν(x) )
∆P ) const η
(18)
with a ) 0 for x > δ.
ν(0) ) 0
(19)
ν(δ), ν′(δ) continuous at x ) δ a-1 is the Brinkman length and has the meaning of characteristic depth for flow penetration into the layer and is, if cylindrical layer forming polymers are considered, approximately given by28
a-1 )
rp 1 - υ 12 υ
(
2
)
with the boundary conditions
ν(0) ) 0
Equation 11 with (12-16) is consecutively solved by a differential method taking as the zeroth approximation the solution of the linear electrostatic problem corrected for the proper boundary conditions. The iteration is stopped if the mean square of the potential difference between subsequent approximations was less than a given position. Having finally obtained the electric potential ψ(x), the spatial charge density due to the distribution of the electrolyte ions inside the layer is given by
Fmob(x) ) NAe0
(23)
(20)
Inserting (17) and the solution of (18) together with (19) (28) Veerapaneni, S.; Wiesner, M. R. J. Colloid Interface Sci. 1996, 177, 45.
ν′(δ) ) continuous ν(∞) ) bounded
(24)
The mobility is corrected for the surface conductivity as follows:
[
bcorr ) b
]
ν1 + ν2 ν1 ν1 + ν2 1 + Rel ν1
1 + Rel(1 - Θ)
(25)
Rel is the dimensionless criterion
Rel ) 2Ks/Kd
(26)
where Ks, K, and d are surface conductivity, bulk conductivity, and particle diameter, respectively. Θ is a coefficient. It expresses the ratio between the noncorrected mobility calculated by means of using the counterion excess charge density instead of the total mobile ion charge density, over the conventional noncorrected particle mobility. u1 and u2 are counterion and co-ion mobility, respectively. Equation 25 is an extension of the HenryBooth concept29,30 of the correction of the electrophoretic mobility for surface conduction. Henry and Booth considered only the continuity of the electric current near the spherical particle surface. In the derivation of eq 25 the continuity of the anion and cation flow was preserved too. Hence, concentration polarization was taken into account. Earlier concepts taking into account concentration polarization were restricted to low potentials.31 Later solutions became available for the case of high surface (29) Henry, D. C. Trans. Faraday Soc. 1948, 44, 1021. (30) Booth, F. Trans. Faraday Soc. 1948, 44, 955. (31) Simonova, T. S.; Shilov, V. N. Kolloidn. Zh. 1986, 48, 370.
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potentials but restricted to the case of a smooth surface.32,33 A new approach was introduced to solve the arbitrary case.34 The asymmetry of eq 25 with regard to co-ions and counterions resulted from the neglect of the contribution of the co-ions to the surface conductivity. The latter assumption is justified for highly charged surfaces and low ionic strengths. In the case of low surface charge density and, consequently, low potentials, the correction (25) is negligible. Illustration of Theoretical Results Charged hairy layers on particle surfaces cause a number of interesting features of the electrophoretic behavior of particles as compared to the model of plane surface charges. It is impossible to provide here a comprehensive overview of the electrokinetics of particles with charged hairy layers. The reader is referred to earlier work where some of the most important characteristics within the limitations of a linear model and without correction for surface conductivity have been discussed already.22 Thus it has been frequently demonstrated that, for example, the electrophoretic mobility is a function of the layer thickness and the hydrodynamic resistance of the layer for hydrodynamic flow. If the Brinkman length is much smaller than the hairy layer thickness, the electrophoretic mobility decreases faster with increasing ionic strengths than for a smooth particle with plane surface charges. If the Brinkman length is comparable with or larger than the hairy layer thickness, i.e., the layer is less dense, a complex dependence of the electrophoretic mobility on ionic strengths was observed. The distribution of charged groups inside the layer is another important parameter. We have shown previously22 that from the shift of the point of zero mobility of the particle some information regarding the charge distribution inside the layer can be obtained. We therefore focus below on the new aspects introduced by considering the nonlinearity of the Poisson-Boltzmann equation. We explore the condition when the correction of the mobility for surface conductance becomes important, and finally we consider the effect of steric mobile ion exclusion from the charged hairy layer. To achieve a clearer representation of the data, it is useful to normalize the electrophoretic mobility for its standard dependence on ionic strength, which is a result of the double layer compression with increasing electrolyte concentration. Let us therefore introduce the apparent charge density, σapp, which is defined as the electrophoretic mobility in a medium with the bulk viscosity η divided by the Debye length, κ-1.
σapp ) bκη
(27)
The term apparent charge density has been chosen because in the case of plane surface charges and low potentials it is indeed equal to the particle surface charge density. If the chemical charge density is known, it indicates how much of the surface charge does not contribute to the mobility as either a result of the layer arrangement, nonlinearity, dissociation, etc. Let us start with the case of a charged layer which has an infinitively high resistance for flow yet ions may penetrate. Such a surface is hydrodynamically equivalent to the classic case of a smooth surface with plane surface (32) Dukhin, S. S.; Deryaguin, B. V. In Electrophoresis; Nauka: Moscow, 1968. (33) Kijlstra, J. In Double layer relaxation in colloids. Thesis, Landbouwuniversiteit Wageningen, 1992. (34) Shilov, V. N.; Zharkikh, N. I.; Borkobskaya, Ju. B. Kolloidn. Zh. 1985, 47, 927.
Figure 1. Theoretical plot of the electrophoretic apparent charge density as a function of pH of a particle covered with a charged layer. Layer parameters were as follows: thickness 4 nm; density of charged sites, 0.03 C/m2; pK ) 5; zero Brinkman length; relative permittivity ) 80. Particle radius 1 µm. No steric exclusion effects. No surface conductivity correction.
charges. The difference, however, comes in when the double layer structure is considered. If the Debye length is small as compared to the hairy layer thickness, most charged groups are screened within the hairy layer and do not contribute to the mobility of the particle. On the contrary, if the Debye length is much larger than the layer thickness, the particle should behave like a plane charged surface. In the intermediate region the particle is subject to a change in the apparent charge density. In Figure 1 we provide the apparent charge density calculated from eq 3 together with (17). The electric potential is given by the solution of (5). The flow field is provided by the solution of (18-19). The apparent charge density of a particle covered with a 4 nm thick charged layer with a homogeneous distribution of fixed charges with a pK of 5 is plotted as a function of pH. For the sake of clarity the surface conductivity correction (25) and the steric ion exclusion (6) are still neglected. As indicated above it is obvious that for the high ionic strengths the apparent charge density is considerably smaller than for low ionic strengths. Even in the case of an ionic strength of only 1 mM the apparent charge density at high pH is only approximately 20% of the layer charge. This is only partly a result of the screening of the fixed charges inside the layer. Additionally, the nonlinearity of the PoissonBoltzmann equation comes into play reducing the particle mobility more effectively at low ionic strengths and high charge density, where the potentials are high. This is nicely demonstrated when comparing the three curves in the range of weak dissociation and, in contrast, in the range of high dissociation. It is worth mentioning that the dependence of the apparent pK on the electric potential causes a small but well-pronounced shift of the halfsaturation value of the mobility toward higher pH with decreasing ionic strength. In Figure 2 we explore the influence of the nonlinearity of the Poisson-Boltzmann equation on the apparent charge density as in Figure 1 and, in addition, the effect of the surface conductivity correction, eq 25. The parameters of the hairy layer are identical to the set used in Figure 1. We provide the calculated apparent charge density as a function of ionic strength expressed in terms of the inverse of the Debye length at pH ) pK and far from the pK. The linear approximation is compared to the nonlinear solution. The latter is derived with and without the correction for the surface conductivity. The picture is quite impressive at conditions of high dissociation at pH ) 9. The linear solution yields a much larger apparent
Electrophoretic Fingerprinting
Figure 2. Effect of nonlinearity and surface conductivity on the apparent charge density as a function of ionic strength. Layer and particle parameters are as in Figure 1.
Figure 3. Effect of layer flow penetrability on the apparent charge density as a function of ionic strength. Other layer parameters are as in Figure 1. pH ) 9.
charge density of the picture than the nonlinear one. The extremum of the linear solution in the region of low concentrations is a result of an increasingly large shift of the apparent pK due to unrealistically high electric potentials. The extremum of the apparent charge density in the case of the nonlinear solution is basically a result of the increasing importance of nonlinearity toward low ionic strength. The correction for the surface conductivity at low ionic strengths is quite important and reduces the apparent charge density at 1 mM by almost 50%. This gives rise to a maximum of the mobility itself. At a smaller degree of dissociation at pH ) pK the surface conductivity correction is less pronounced. Here only the nonlinearity is of some importance yielding a reduction of the mobility of the order of 15%-30%. This effect can be partly explained by the effect of the potential itself. Equally important is the indirect effect of the nonlinearity on the real charge density. At pH ) pK the effect of the electric potential on the state of dissociation is most pronounced because the slope of the titration curve is at minimum at pH ) pK. For this reason relatively small changes of the potential result in a pronounced effect upon the group dissociation equilibrium. To summarize Figure 2, it can be concluded that both nonlinearity and surface conductivity provide an important influence on the mobility (apparent charge density) of particles with charged hairy layers. In Figure 3 we provide the effect of the hydrodynamic flow inside the hairy layer on the apparent charge density taking into account the surface conductivity correction (eq 25) but still neglecting steric exclusion of mobile ions
Langmuir, Vol. 13, No. 20, 1997 5299
Figure 4. Effect of steric mobile ionic exclusion on the apparent charge density as a function of ionic strength. Radius of layer forming polymers 0.5 nm, 25% volume occupation. Brinkman length as given by eq 20. Other layer parameters are as in Figure 1. pH ) 9.
(eq 6). As a measure of the hydrodynamic resistance of the layer we varied the Brinkman length a-1. In addition to the case of a-1 ) 0 two different finite penetration depths of flow were considered. It can be seen that especially at high ionic strengths the apparent charge density is very sensitive to the variation of the Brinkman length. Characteristic flow penetration depths of a few angstrom can result in a large effect on the particle mobility resulting in a pronounced increase of the apparent charge density with increasing Brinkman length. This is a result of the fact that the electroosmotic flow inside the hairy layer is much less subject to the double layer compression with increasing ionic strength than the respective electroosmotic flow in front of a smooth surface. It is worth noting that at low ionic strengths all curves tend to coincide. In this region the charged hairy layer is thin compared to the Debye length and the system becomes increasingly independent of hydrodynamical properties of the charged hairy layer. A new aspect is introduced in Figure 4. Here we explore the importance of the steric exclusion of mobile ions from the charged hairy layer for the electrophoretic behavior, eq 6. To our knowledge this has not been considered before in the context of electrophoresis. The steric exclusion may be both nonspecific and ion specific. The nonspecific effect is explained as follows: Naturally, the part of the volume of the charged hairy layer occupied by polymer chains is not accessible for mobile ions. This gives rise to an effectively reduced ion concentration inside the hairy layer which in turn results in an increased electric potential due to a decreased screening capability of the mobile ions.27 The mesh size of the hairy layer is important for ionspecific exclusion effects. If the mesh size is not much larger than the mobile ion diameters, a different partition coefficient is observed for co-ions and counterions provided their radii are not equal. The larger species is more efficiently excluded from the layer. In Figure 4 we explore the steric exclusion effect upon the apparent charge density of a charged homogeneous hairy layer with 25% volume occupied by polymers of 1 nm in diameter. At medium and high ionic strengths the pure volume effect alone increases the apparent charge density by approximately 15%. Even the specific effect of both the small ions Na+ and Cl- can be seen. The complete or gradual exclusion of, for instance, the cation may result in a remarkable increase of the apparent charge density. In Figure 5 we provide evidence that a neutral layer of adsorbed polymers can be charged due to ion exclusion. The ion with the larger size is more effectively
5300 Langmuir, Vol. 13, No. 20, 1997
Donath et al.
Figure 5. Ion exclusion induced charging of a neutral polymer layer. Effect on the apparent charge density as a function of ionic strength. 25% polymer occupied volume, polymers are 0.5 nm in radius, layer thickness is 4 nm.
excluded from the neutral hairy layer thus causing an effective charge due to the incorporation of the smaller ion. While NaCl in the surrounding solution should result in a small positive charge of the hairy layer, an increase in the cation size would result in a negative apparent charge density. In the limiting case of a totally excluded cation, an apparent charge density of the order of -10-2 C/m2 can be reached. This corresponds to an electrophoretic mobility as high as -0.92 × 10-8 m2/(V s) at 150 mM ionic strength. Typical for this exclusion-caused surface charge is the increase of the charge with increasing ionic strengths. In practice it might be difficult to distinguish this behavior from charging by means of adsorption. Molecular Considerations Given the considerable number of parameters determining the electrophoretic behavior of particles covered with the adsorbed PAH and PSS, it is desirable to have as much as possible structural information regarding the parameters of the adsorbed layers. It is therefore useful to look into molecular details of the employed polyions. Figure 6 provides a graphical representation of decameric PSS and PAH as constructed by using the molecular modeling package Insight II, release 95.0, Biosym/MSI. Monomer units were obtained from the fragment library of Insight II and repeated in isotactic (A) as well as in syndiotactic (B) conformation to model idealized representative structures of the polymers in an extended state. This was accomplished by adjusting the two repeating backbone dihedral angles in agreement with allowed dihedral states to -60° and 180° in an alternating fashion (A) and to 180° throughout the entire fragment (B). The side chains were positioned by selecting standard rotamer dihedral angles such that no steric overlap occurred. None of the structures displays steric overlap within a 0.2 Å tolerance distance. Bond lengths and angles were taken as given in Insight II. The isotactic form of both polymers possesses a screw axis with a characteristic repeat length of 6.2 Å corresponding to 2.6 Å rise per monomer and a 120° progression angle per monomer. For PSS, conformations with stacked aromatic rings are also possible. The 120° periodicity and the ring stacking are sterically impossible for the syndiotactic form. Here a rather flat conformation is adopted. The identical repeat length of the monomers suggests that electrostatic interactions of the charged groups could induce effective ion pair formation. However, not all but at most 2/3 of the charges of a single isotactic polymer can be used for the pair interaction.
Figure 6. Representation of the molecular shape of poly(allylamine) and poly(styrenesulfonate). Upper rows show the polymers in wireframe representation viewing perpendicularly to the screw axis. Lower rows: Cross-sectional view along the screw axis. van der Waals surfaces are depicted by dots. The corresponding radii were taken from the standard radii used in Insight II. Distance measures correspond to the radial dimensions of the polymers. (A) Polymers in an isotactic form, i.e., side chains are bound to the main chain carbon atom with the same chirality. (b) Syndiotactic form, i.e., alternating chirality of the carbon atoms to which the side chain is attached.
In the syndiotactic conformation a more efficient pair interaction using the majority of charges seems sterically possible. This however, would not be a favorable situation for multilayer building. It is important for the subsequent considerations that the PSS charged groups extend further from the polymer axis. Due to the strong intramolecular mutual repulsion of the side chains both electrostatically as well as sterically especially PSS should preserve a
Electrophoretic Fingerprinting
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relatively stiff shape. PAH is capable of nicely fitting into the shallow grove of both isotactic and synodiotactic PSS. The thickness of the docked complex of PSS together with PAH seems to be about 2 nm thick given some thermal fluctuations of the docked complex. Therefore, in the adsorption layer the assumption of a homogeneously smeared out charge seems to be appropriate. First, one has to bear in mind that the side chains are probably random. Both examples in Figure 6 represent the limiting possible shapes. Second, thermal fluctuations smear out the charge, and third, since the layer thickness is smaller than or comparable with the Debye length, the details of the charge arrangement within such a thin layer do not significantly modify the resulting electrophoretic mobility. Thus, it is reasonable to describe the “hairs” as uniformly charged with a diameter of r ) 1 nm. Experimental Section Materials and Methods. Particles. The polystyrene latex particles (mean diameter 600 nm) with carboxyl and sulfate groups on the surface serving as the basic surface for polymer coating were kindly provided by Dr. B. R. Paulke (Max-PlanckInstitut fu¨r Kolloid- und Grenzfla¨chenforschung, Teltow-Seehof). Details of the particle preparation are described elsewhere.35 Polymers. Positively charged poly(allylamine) hydrochloride (PAH, Mw ) 50000-60000) and the negatively charged poly(styrenesulfonate) sodium salt (PSS, Mw ) 70 000) were obtained from Aldrich (Sternheim, Germany). The batch of PAH 7155012-4 was used without further purification. To remove short PSS molecules, the material was dialyzed against water: An aqueous PSS solution was dialyzed for 2 days in a dialysis tube (VISKING 27132, Roth, Germany) and subsequently freeze-dried. Adsorption of Polymers. The adsorption of polymers onto latex particles has been performed as follows: For PAH, 200 µL of latex particle solution (4.9% v/v) was added to 2 mL of salt free PAH solution (pH 5) to reach a final monomer concentration of 10-2 M. The polymer was allowed to interact with the latex surface for 30 min at 25 °C. Finally the particles were washed twice with distilled water (pH 7) before measuring electrophoretic fingerprints. For PSS, the pellet of PAH-coated latex particles was resuspended in 2 mL of salt free 10-2 mol/L PSS solution. It was kept for 30 min at 25 °C before two subsequent washings in distilled water (pH 7) and electrophoretic fingerprinting. Subsequently, in a similar manner the final PAH coating was performed. Electrophoretic Measurement. Electrophoretic mobility (EPM)-pH curves and electrophoretic fingerprints were measured with the ELECTROPHOR automated electrophoretic analyzer which has been described in detail elsewhere.36 Essentially, the instrumentation is based on a real-time image processing system combined with a special tracking procedure which allows measurement of mean values of the electrophoretic mobility and fingerprints (simultaneous measurements of the electrophoretic mobility in dependence on pH and conductance of the electrolyte over a wide range) in combination with a simultaneous particle discrimination based on other parameters such as size, sedimentation rate, optical density, and shape of the individual particles. The mean mobility was reproducible to better than 2%. Electrophoretic measurements were made in NaCl solutions with different salt concentrations in the range of 0.1-150 mM corresponding to a conductance of 0.2-15.0 mS/ cm. To obtain the EPM-pH curve at a given ion concentration took not more than 20 min. The titration changes the ionic strength, which is especially important at low salt concentrations. Therefore the conductivity of the sample is continuously monitored. From the conductivity data the ionic strength was calculated on the basis of tabulated ion mobilities and known solution composition. If we speak below of “high mobility”, we mean the absolute of the mobility irrespective of its sign. (35) Paulke, B.-R.; Mo¨glich, P.-M.; Knippel, E.; Budde, A.; Nitzsche, R.; Mu¨ller, R. H. Langmuir 1995, 11, 70. (36) Gru¨mmer, G.; Knippel, E.; Budde, A.; Brockmann, H.; Treichler, J. Instrum. Sci. Technol. 1995, 23, 265.
Figure 7. Electrophoretic fingerprint of charged polystyrene latex particles.
Experimental Results Let us start with the presentation of the fingerprints of the various consecutively deposited layers onto the charged polystyrene latex support. Before we try to understand the experimental fingerprints by means of applying the above derived theoretical framework, we first present the experiments alone summarizing the most informative features for the subsequent analysis. A choice has to be made whether to use the mobility or the above introduced apparent charge density. Although we generally prefer the latter form for the comparison with the theoretical predictions, we first show the original data. It has to be, however, realized that the interpretation of the mobility in terms of apparent charge density would increase the impact of the high ionic strength region of the fingerprint, which as shown above is most sensitive to the layer characteristics. In Figure 7 we show the fingerprint of the electrophoretic mobility of the naked latex particle. There are a number of interesting features: While the decrease of the mobility toward more negative values with increasing pH is expected, it is somewhat surprising that the mobility changes over such a broad pH range. Up to pH values of 6 and 7 the dissociation of surface bound ionogenic, probably carboxyl groups seems to be incomplete. Such a behavior indicates a broad distribution of the pK values of the individual surface groups. Another characteristic feature of the naked latex particle fingerprint is that the mobility is almost independent of the ionic strength at a constant pH. One would expect a quite pronounced increase of the mobility with decreasing ionic strength. Yet especially in the pH regions of mobility saturation flat surfaces of the fingerprint are found. One has to bear in mind that such a behavior would translate into a pronounced increase of the apparent charge density with increasing ionic strengths. There are two more important findings: At low pH values a mobility reversal is observed indicating the presence of positive charges at the latex surface. Equally important is the pronounced dependence of the point of zero mobility on ionic strength. Over the
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Figure 8. Electrophoretic fingerprint of polystyrene latex particles coated with poly(allylamine).
ionic strength range investigated (from 3 to 150 mM NaCl) the zero point of mobility is shifted toward basic pH by more than two pH units. As reported previously22 in the framework of the charged hairy layer model this indicates either adsorption of cations or a density profile of the positive groups toward the water adjacent side of the charged hairy layer. However, such a large shift of the zero point of mobility can hardly be explained by a density profile alone. Thus we may conclude that adsorption of cations to sulfate or carboxyl groups is the major process responsible for the shift of the point of zero mobility. This conclusion is supported by the reversal of the latex charge at low pH. In Figure 8 we show the fingerprint after the deposition of the first PAH layer onto the latex surface. Except at pH values above approximately 8, the surface appears to be positively charged as a result of the adsorbed polycation layer. Figure 8 further suggests that to a certain extent the underlying latex surface charges contribute to the electrophoretic mobility. This can be inferred both from the negative mobility at basic pH and from the continuous change of the mobility over a broad pH range. The quantitative contribution from the charge of the latex support can be estimated from the value of the negative mobility at basic pH. Here PAH is likely to be deprotonated and we see approximately 1/3 of the negative mobility of the naked latex. The curve of zero mobility in Figure 8 is inclined toward smaller pH with increased salt concentration (in contrast to the previous picture) indicating anion adsorption. The mobility dependence on ionic strengths is again remarkably flat except in the region of high ionic strengths at low pH. In the pH range between 8 and 9 we observe the deprotonation of the amino groups in the fingerprint as a small but well pronounced step toward more negative mobilities. We also varied the concentration of the PAH in bulk during deposition. Remarkable was that even a 10-fold decrease of the PAH concentration from 10-2 to 10-3 monoM did not change the resulting mobility. Furthermore, prolonged incubation in PAH free medium did not lead to a reduction of the mobility thus clearly indicating an irreversible adsorption. With a deposition of a subsequent PSS layer a very
Donath et al.
Figure 9. Electrophoretic fingerprint of polystyrene latex particles coated consecutively with poly(allylamine) and poly(styrenesulfonate).
pronounced overall negative surface charge is observed (Figure 9). One measures remarkably high mobilities up to -6 × 10-8 m2/(V s) at low ionic strengths and high pH. This change of sign of the mobility has been recently measured and is considered to be a characteristic feature of polyion adsorption although thermodynamically not yet fully understood.8,18 Nevertheless, the influence of the PAH can be inferred from the slightly positive mobility at low pH where the dissociation of the sulfonate groups is reduced. The curve of zero mobility is by no means parallel to the conductivity axis thus indicating again a well-pronounced adsorption of cations as discussed above in connection with the naked latex fingerprint. Remarkable is further the continuous decrease of the mobility as a function of increasing pH leading to the conclusion that still the naked latex surface is electrophoretically visible. When again a PAH layer is deposited onto the latex/ PAH/PSS system we deduce from Figure 10 a mostly positive surface but characterized by a smaller average mobility as compared to the case of PAH adsorption onto the initial latex particle. At higher pH the system appears to be more negative than in Figure 8. The proton association equilibrium is clearly seen between pH 8 and 9. The dissociation equilibrium of the sulfonate groups is inferred from the sharp step around pH 4. The curve of zero mobility is a more complex function of the conductivity and not as pronounced as in the case of PSS being the top layer although it can be seen that it is inclined toward lower pH values with increasing ionic strength. This indicates similar to Figure 8 an adsorption of chloride ions to the positively charged top layer. It is again worth mentioning that the mobility as a function of ionic strengths is flat, at least in the region of intermediate and high pH. Comparison of Theoretical and Experimental Fingerprints. Our aim is to provide a theoretically based description of the experimental fingerprints to arrive at a quantitative picture of the surface properties of the polyion-covered latex particles. To this end we tested a
Electrophoretic Fingerprinting
Figure 10. Electrophoretic fingerprint of polystyrene latex particles coated consecutively with poly(allylamine), poly(styrenesulfonate), and again poly(allylamine).
number of physicochemically based assumptions regarding the charged layer structure to achieve a good quantitative agreement between theory and experiment. Given the large number of variables and the numerical character of the theory, a fitting in the mathematical sense is not meaningful. Especially, one cannot expect a good fit over the whole range of the fingerprint because the structural parameters of the layers can (and probably must) change as a function of pH and ionic strength. Both parameters modify the extent of the electrostatic interaction within the layer, which is known to be very significant for the layer-by-layer polyion adsorption. Let us start with an analysis of the latex particle surface. Although the aim of this paper is not to investigate the nature of the latex particle surface we still need a proper phenomenological description. Otherwise it will not be possible to explore the adsorbed polyion layers. It is now well accepted that latex particles have a hairy surface. It is very difficult to understand their electrophoretic behavior in the framework of the Smoluchowski theory which is valid for smooth surfaces with plane surface charges. This is seen when theoretical and experimental fingerprints are compared. As mentioned already in the Experimental Section, the mobility at high ionic strength is too large as compared with low ionic strengths to fit into a model of plane surface charges or of a charged hairy layer with zero Brinkman length, respectively. Attempts to explain the behavior with a decreased dielectric permittivity inside the layer also failed. From the beginning, it was obvious that cation adsorption had to be present because at low pH positive mobilities are recorded. The existence of some positive groups is highly unlikely for chemical reasons. The positive charge of the naked latex at low pH further depends on the composition of the bulk electrolyte. Moreover, at high pH no titratable groups are seen. After a number of calculations probing a large variety of parameter combinations it appears that one possibility to explain the latex fingerprint was to assume an approximately 3 nm thick charged hairy layer
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Figure 11. Three-dimensional comparison in terms of apparent charge density between the theoretical fingerprint (grid) and the latex electrophoretic mobility data (filled circles). Parameters for the theoretical surface are as follows: charged sites, density 0.04 C/m2, pK ) 4.5, density distribution 1 - (x/δ)2; and density 0.05 C/m2, pK ) 6.5, density distribution 1 - (x/δ)2. Adsorption sites: density 0.04 C/m2, cation adsorption constant 100/M, homogeneous distribution. Layer thickness 3 nm. Brinkman length 1.34 nm. 85% ion-accessible volume within the layer, layer hairs 0.5 nm radius.
with relatively low frictional resistance for flow yielding a Brinkman length of 1.3 nm. An alternative explanation was to assume a hairy layer of 1-0.5 nm but with a different density of anionic groups.37 Due to the combined influence of hairy layer thickness, Brinkman length, and charge density it is not always possible to unambiguously find the layer thickness, especially if the electrostatic parameters of the hairy layer are less well known. The charged groups have to have a broad pK in the range from 4.5 to 6.5 which we attribute to the existence of carboxyl groups. The distribution of the pK may be a result of the different local environment of the charged surface groups of the latex. Adsorption of cations with an adsorption constant of 100 M-1 is necessary too. Figure 11 provides the comparison between experiment and theory. The details of the layer parameters are given in the legend. The theory fits nicely at high ionic strengths. The experimental curves at low ionic strengths are slightly lower than the theoretical three-dimensional plot. This small difference may be the result of a certain flexibility of the hairs at the latex surface. If, for instance, a charge distribution with a center toward the solution adjacent side of the hairy layer is used, the low ionic strength curves lay on the theoretical plot. Such a change of the arrangement of the charged groups attached to the hairs as a function of the ionic strengths is not unexpected since the less effective electrostatic screening at low ionic strengths favors a mutual repulsion of the hairs resulting in some swelling of the charged hairy layer.38 The latex particle surface appears to be highly charged. The fixed charge density sites have an overall surface concentration of 0.09 C/m2. Reduction of the charge density and, additionally, the hairy layer thickness yields comparatively good fits. On the basis of the available data it (37) Donath, E.; Budde, A.; Ba¨umler, H.; Knippel, E. Submitted for publication in Colloids Surf. (38) Donath, E.; Voigt, A. J. Theor. Biol. 1983, 101, 569.
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Figure 12. Three-dimensional comparison in terms of apparent charge density between the theoretical fingerprint and the sulfate latex PAH covered electrophoretic mobility data. Parameters for the theoretical surface: Latex surface same as in Figure 11, except a homogeneous site distribution and no adsorption was assumed. PAH charges: density ) 0.03 C/m2, pK ) 9, and density ) 0.03 C/m2, pK ) 10, both distributions homogeneous. PAH layer thickness 1 nm. Adsorption sites in the PAH layer, density ) 0.04 C/m2, anion adsorption constant 100/M, homogeneous distribution. Brinkman length is 1.34 nm. 85% ion accessible volume within the layer, layer hairs 0.5 nm radius.
appears to be impossible to unquestionably deduce the latex hairy layer thickness. Our conclusion is that, nevertheless, the charges are arranged in a loose layer with a possibly more pronounced orientation toward the bulk at low ionic strengths. Figure 12 represents an attempt to describe the electrophoretic fingerprint of the first adsorbed PAH layer. We find good coincidence between experiment and theory except at low pH if a 1 mm thick adsorbed hairy layer is assumed, which presumably consists of PAH. The pK is in the range between 9 and 10. The Brinkman length is comparable to that of latex hairy layer. In contrast to the naked latex surface, it is necessary to assume adsorption of anions with an adsorption constant of the order of 100 M-1. Note that no cation adsorption is observed, even though cation adsorption seems to be an important property of the naked latex surface. The charge density of the adsorbed PAH is about 0.06 C/m2. The divergence between the theoretical and the experimental plot at low pH which is observed at any ionic strength is easily understood. Here the underneath latex charges are not dissociated and thus free some PAH charges, which have been immobilized by ion-pair formation with the latex charged groups at higher pH. This is a typical behavior as demonstrated further below. These additional PAH charges together with the above “free” 0.06 C/m2 provide a total charge density of the PAH layer comparable with the one of the naked latex surface. Yet it cannot be ruled out that the seemingly increase of the apparent charge density at low pH is caused by structural alterations of the adsorbed PAH layer due to the decreased electrostatic attraction toward the less charged latex surface. To summarize, the situation seems to be as follows: The PAH largely replaces the adsorbed cations from the latex surface. The PAH layer is too thin to be capable of hydrodynamically screening the latex surface charges. The
Donath et al.
Figure 13. Three-dimensional comparison in terms of apparent charge density between the theoretical fingerprint and the sulfate latex PAH-PSS covered electrophoretic mobility data. Parameters for the theoretical surface: Latex surface same as in Figure 12. No PAH charges. PAH layer thickness ) 1 nm. No adsorption of anions to PAH. PSS charges: density ) 0.03 C/m2, pK ) 3.5, homogeneous distribution, layer thickness 1 nm. Adsorption sites in the PSS layer, density ) 0.04 C/m2, cation adsorption constant 100/M, homogeneous distribution. Brinkman length 0 1.34 nm. 85% ion-accessible volume within the layer, layer hairs have 0.5 nm radius.
picture is not consistent with a few nanometer thick PAH layer. This does not necessarily rule out the possibility that a few tails dangle further into the solution. It is further remarkable that by far not all latex charges found counterparts of adsorbed PAH charges. Also the majority of the charges of the adsorbed PAH are not in direct contact with carboxyl groups of the latex. But about 1/3 of the PAH charges do form ion pairs with these groups and only became electrophoretically active after protonation of the carboxyl groups. It is also likely that the coverage of the latex surface by adsorbed PAH is not complete. This may be an explanation for a Brinkman length comparable to the hairy layer thickness. Figure 13 analyzes the next PSS layer on top of the already adsorbed PAH. The picture is qualitatively similar to the previous case. However, we now see an apparent increase of the PSS charge at high pH of approximately 1/3 of the value seen at lower pH. Here the deprotonation of the PAH charge at high pH frees some of the PSS groups, fixed before to the surface by ion-pair formation. This again is evidence for the close electrostatic interaction between PSS and PAH within the adsorbed layers. It is worth noting that the PSS charge density is apparently higher than the PAH charge which is easily understood if the molecular structures of both polymers are considered. The PSS charges cannot be as effectively compensated by PAH because PSS may more or less enclose the smaller PAH. The pK of PSS is between 3.5 and 4.5. Again, there is evidence for an adsorption of cations to PSS. In contrast, the anions adsorbed to PAH in the previous layer seem to be largely replaced by the PSS charged groups. Figure 14 demonstrates that the influence of the next PAH layer is fully consistent with the previous results. Again we see the characteristic release of some apparent extra charges at low pH indicating the ion-pair formation of approximately 1/3 of the polyion charges. The electrophoretic fingerprint is consistent with the assumption of
Electrophoretic Fingerprinting
Figure 14. Three-dimensional comparison in terms of apparent charge density between the theoretical fingerprint and the sulfate latex PAH-PSS-PAH covered electrophoretic mobility data. Parameters for the theoretical surface: Latex surface same as in Figure 12. First PAH layer has no charges. PSS charges: density ) 0.005 C/m2, pK ) 3.5, homogeneous distribution, layer thickness 1 nm. No adsorption to PSS. Outermost PAH layer charges: density 0.02 C/m2, pK ) 9, density ) 0.02 C/m2, pK ) 10, both distributions homogeneous. Layer thickness 1 nm. Anion adsorption sites in the outermost PAH layer density ) 0.05 C/m2, adsorption constant ) 100/M, homogeneous distribution. Brinkman length is 1.34 nm. 85% ion-accessible volume within the layer, layer hairs have 0.5 nm radius.
1 nm layer thick hairy layer. Again the results are inconsistent with a thickness of a few nanometers. Remarkable is that still the latex charge forms a significant part of the electrophoretic effective charge. This is inferred from the broad pK-dependence. We favor a picture of polymer free spots at the surface which might be too small in diameter to provide a possibility for further ion-pair formation between polyanions and polycations, especially, since the binding energy per ion pair is only of the order of kT.18 The interpretation of the fingerprints does not require interpenetration of the charged polymer layers. On the other hand it cannot be ruled out either. The interpenetration concept of polymers would result in an effective decrease of the charge density per layer, which we indeed observe. It also would allow for the influence of the latex hairs. The electric potential values at the outer border of the system latex-PAH-PSS-PAH vary between 51.4 and 33 mV in dependence of pH and ionic strength. This order of magnitude is in good agreement with potentials derived from surface forces experiments.18 Concluding Remarks Clearly further experimental studies are necessary in this direction. It would be quite interesting to control the polymer charge density and to vary the polymer molecular shape. The latex surface used here is rather complex. A more smooth surface as a support for the polyion layerby-layer adsorption would be desirable. During the experiments we discovered the problem that earlier charges of PAH supplied by the manufacturer
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differed considerably from those obtained recently. With the old polyelectrolyte that was used here to derive Figures 8-10 only a slightly positive charge of the outer surface was measured with potential sensitive probes if the outer surface nominally existed of PAH.15 This is in agreement with the results of this work demonstrating that for pH ∼ 7 the electrophoretic mobility is only slightly positive (Figures 8 and 10). With the recently purchased PAH the charge reversal was stronger and nearly symmetrical with each deposition. This was also measured by surface force experiments.18 Nevertheless, the qualitative results concerning the thickness of the hairy layer, the ion-pair formation, and the cation and anion adsorption are maintained. Another possibility to investigate in the future is that stereoisomeric effects are important. As demonstrated above, the arrangement of the substituents has a pronounced influence on the molecular three-dimensional shape. It has to be expected that the efficiency of intermolecular docking is sensitive to these configurational properties of the polyions. Further studies devoted to the investigation of the importance of stereoisomeric forms are desirable. The electrophoretic fingerprints in Figures 8-10 clearly elaborate on conditions to prepare multilayer, i.e., to maximize the distance from the curve of zero mobility in the pH, conductivity plane. Although we could recently show that multilayers with small layer numbers (∼3) can also be grown without charge reversal,18 the latter is inevitable to prepare thick multilayers as was achieved with the system under study.5,6 An interesting issue suggested in the theoretical part is the charge density of porous surfaces caused by the steric ion exclusion. It seems to be an important effect worth separate study. Frequent difficulties in the understanding of the electrophoretic behavior of particles with porous surfaces might have been also associated with this particular effect. We are aware of the fact that the large number of unknown parameters in explaining the fingerprints may be the cause of a certain arbitrariness of the chosen sets of parameters. For example, slightly modifying the charge density distribution could be equivalent to a small layer thickness change or a small change in flow penetration. Thus the layer thicknesses of 1 nm given above can easily vary between 0.7 and 1.3 nm to yield similar good fits. But, once more, a few nanometer thick hairy polyion layer would be inconsistent with the experimental fingerprint. However, the fits are quite sensitive to the charge density. It might be worth combining electrophoretic studies with dielectric relaxation methods, such as low-frequency dielectric spectroscopy or electrorotation. Additional information concerning the behavior of mobile ions inside the polyelectrolyte layer may be obtained. In summary we hope that the achievements in the interpretation of electrophoretic behavior of particles with adsorbed polyelectrolytes made in this study give rise to further applications of electrokinetics to hairy particles. Acknowledgment. We appreciate that Frank Essler dialyzed the PSS. We acknowledge the support of grants of the Deutsche Forschungsgemeinschaft (Do 410/2-1, Kn 384/2-2, He 1615/5-2, He 1616/7-1). We are further indebted to the SFB 262 (project D13/D19). We enjoyed the hospitality of M. Schmidt. LA970090U
